Question

find the distance between the two points (2,3) and (7,7).

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Identify the coordinates

Here $x_1 = 2,y_1 = 3,x_2=7,y_2 = 7$.

Step3: Substitute values

$d=\sqrt{(7 - 2)^2+(7 - 3)^2}=\sqrt{5^2+4^2}$.

Step4: Calculate squares

$d=\sqrt{25 + 16}$.

Step5: Sum inside square - root

$d=\sqrt{41}$.

Answer:

$\sqrt{41}$